Defect Dynamics in 2D MoS
2
Probed by Using
Machine Learning, Atomistic Simulations, and
High-Resolution Microscopy
Tarak K. Patra,
Fu Zhang,
,§
Daniel S. Schulman,
Henry Chan,
Mathew J. Cherukara,
,
Mauricio Terrones,
,§,#,
Saptarshi Das,*
,§,
Badri Narayanan,*
,,
and Subramanian K. R. S. Sankaranarayanan*
,,&
Center for Nanoscale Materials,
Materials Science Division, and
X-ray Science Division, Argonne National Laboratory, Argonne,
Illinois 60439, United States
Materials Science and Engineering,
§
Center for 2-Dimensional and Layered Materials,
#
Department of Physics,
Department of
Chemistry, and
Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park,
Pennsylvania 16802, United States
&
Computational Institute, University of Chicago, Chicago, Illinois 60637, United States
*
S
Supporting Information
ABSTRACT: Structural defects govern various physical, chemical, and
optoelectronic properties of two-dimensional transition-metal dichalcoge-
nides (TMDs). A fundamental understanding of the spatial distribution and
dynamics of defects in these low-dimensional systems is critical for advances
in nanotechnology. However, such understanding has remained elusive
primarily due to the inaccessibility of (a) necessary time scales via standard
atom istic simulations and (b) required spatiotemporal resolution in
experiments. Here, we take advantage of supervised machine learning, in
situ high-resolution transmission electron microscopy (HRTEM) and
molecular dynamics (MD) simulations to overcome these limitations. We
combine genetic algorithms (GA) with MD to investigate the extended
structure of point defects, their dynamical evolution, and their role in
inducing the phase transition between the semiconducting (2H) and
metallic (1T) phase in monolayer MoS
2
. GA-based structural optimization
is used to identify the long-range structure of randomly distributed point defects (sulfur vacancies) for various defect
densities. Regardless of the density, we nd that organization of sulfur vacancies into extended lines is the most
energetically favorable. HRTEM validates these ndings and suggests a phase transformation from the 2H-to-1T phase
that is localized near these extended defects when exposed to high electron beam doses. MD simulations elucidate the
molecular mechanism driving the onset of the 2H to 1T transformation and indicate that nite amounts of 1T phase can
be retained by increasing the defect concentration and temperature. This work signicantly advances the current
understanding of defect structure/evolution and structural transitions in 2D TMDs, which is crucial for designing
nanoscale devices with desired functionality.
KEYWORDS: machine learning, microscopy, atomistic simulations, 2D materials, phase transitions, and defect dynamics
T
ransition-metal dichalcogenides (TMDs) exhibit ver-
satile electronic properties and, in turn, have attracted
tremendous attention for possible applications in
nanoscale electronic devices.
14
In these 2D-TMDs, a myriad
of structural defects can either pre-exist or be introduced
during sample preparation, processing, and transfer processes.
These defects can be points (e.g., chalcogen vacancies) or of
extended kind ( e.g., dislocations and boundaries); they are
known to have a profound inuence on the physicochemical,
electronic, and optical properties of these materials.
5,6
For
example, electrical-transport measurements on thin sheets of
MoS
2
almost universally reveal n-type eld eect transistor
(FET) characteristics, largely owing to the presence of
chalcogen vacancies, impurities, and metal-like antisite defects
that pin the Fermi level of the metal at the metal/TMD
contact interfaces.
710
In addition, a high defect density is
strongly correlated with low carrier mobility
1113
as well as
Received: April 16, 2018
Accepted: August 3, 2018
Published: August 3, 2018
Article
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hysteresis in FET characteristics, since they act as adsorption
sites for chemical spe cies. While defects are considered
detrimental for conventional high-performance electronic
devices, precise control over the density and distribution of
defects may open up avenues for electronic applications, such
as neuromorphic devices.
14,15
Previous experimental and theoretical studies suggest that
the most abundant defect in TMDs, such as MoS
2
, is the
chalcogen (sulfur) monovacancies. These point defects often
reorganize to form extended structures during sample
processing, transfer, as well as operation of a device; atomic-
scale dynamics of these extended defect structures control key
structural transitions.
16
Of particular interest is the defect-
mediated crossover between 2H (semiconductor) and 1T
(metallic) phases of MoS
2
mainly owing to its immediate
relevance to nanoscale device applications.
1719
The reorgan-
ization of point defects necessary for 2H-to-1T transition can
be triggered via operating/processing conditions of heating,
prolonged-electron beam irradiation, or lithiation.
1719
Struc-
turally, 2H phase possesses a trigonal prismatic arrangement of
a molybdenum (Mo) atom sandwiched between two sulfur (S)
atoms, while the 1T phase exhibits an octahedral coordina-
tion.
20
In addition to dierent electronic properties, the two
phases also exhibit contrasting magnetic behavior; 1T phase is
paramagnet, while 2H phase is weakly diamagnetic.
21
A precise
control over this phase transition is of great interest to make
specic spatial patterns of 1T/2H domains, such as placing low
resistance 1T phase electrical contacts with an atomically sharp
interface to the semiconducting 2H channel in FETs.
22
The
2H and 1T phase can coexist in a single-layer MoS
2
, and the
relative fractions can be varied to tune their optoelectronic and
electrocatalytic properties. For example, when the contents of
the 1T phase increase, the photoelectric conversion eciency
of a MoS
2
-based photo anode increases,
23
the performance of a
MoS
2
based supercapacitor improves,
24
and the eciency of
WS
2
nanosheets for hydrogen evolution reactions (HER) is
enhanced.
25
Interestingly, the defect distribution in a Li-
intercalated MoS
2
sheet can also be altered by sonication
26
and
solvent thermal treatment to reverse the transformation from
the 1T to the 2H phase.
27
Evidently, a fundamental
understanding of the atomic-scale structure and dynamics of
defects in 2D TMDs as well as their role in phase transitions is
very crucial for device applications. However, such an
understanding has remained elusive until now.
The transition between 2H and 1T phases involves local
rearrangement of S atoms with respect to their central Mo
atom. A previous study on Re-doped MoS
2
reports that the
2H-to-1T transition proceeds via formation (and subsequent
intersection) of an intermediate alpha (α) phase under
electron-beam radiation at high temperatures.
16
Although
this work characterized the structure of α-phase to contain a
shrunk zig-zag pattern of Mo atoms,
16
the key question as to
why such an intermediate phase is required for the 2H to 1T
phase transformation remains unanswered. Recent density
functional theory works have shown that the 2H-to-1T phase
transition is associated with a nite energy barrier, with 2H
being the energetically most favorable phase;
28
they postulate
that the electron transfer between MoS
2
and the dopants
initiate the 2H-to-1T transformation.
29
However, the molec-
ular mechanisms underlying the 2H-to-1T transition, the role
of defects, as well as the dynamical evolution/rearrangement of
S and Mo atoms during this phase transformation have not yet
been established. The major challenge in addressing these
questions is that the atomic-scale processes governing
formation of extended defects, and phase transition involves
a broad range of time scales from picoseconds to several
seconds or minutes. The shorter time scales (picoseconds) can
be accessed via ultrafast synchrotron X-ray experiments, such
as coherent diraction imaging. Although our recent study
using coherent diraction imaging at state-of-the-art synchro-
tron facilities has been successful in investigating multilayered
2-D dichalcogenides,
30
the spatial resolution is limited to 10
Figure 1. Evolutionary search for optimal extended defect congurations at various concentrations of S vacancies, achieved using genetic
algorithms. (a) Potential energy of the most stable conguration is plotted as a function of generation at various defect concentrations. The
defect concentration is evaluated as the fraction of the available S sites that are vacant. The initial and nal congurations of four evolutions
are shown in (b), (c), (d), and (e) for concentrations of 1.5%, 4.0%, 5.0%, and 7.5%, respectively.
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nm, which makes it dicult to track point defects. High-
resolution transmission electron microscopy (HRTEM), on
the other hand, possesses the necessary resolution to image
point defects; but cannot capture ultrafast dynamics owing to
its slow frame speed (10 Hz). Standard atomistic simulations
(e.g., molecular dynamics) have atomic resolution but are
limited to several tens of nanoseconds.
Here, we use machine learning, molecular simulations, and
high-resolution transmission electron microscopy (HRTEM)
to overcome these limitations. We investigate the energetics of
arrangement of point defects into extended line defects at
various S-vacancy concentrations and subsequently elucidate
the role of these extended defects in the 2H-to-1T phase
transformation. A genetic algorithm (GA) is used to eciently
search the most energetically favorable distribution of atomic
defects, wherein the energies of individual candidate structures
(genes) are calculated using a reactive force eld. The stable
structures identied by our evolutionary search are exper-
imentally veried via HRTEM. We then investigate the gliding
and rearrangement of S and Mo atoms around the regions of
extended defects in the MoS
2
layer via molecular dynamics
(MD) simulations. These MD simulations identify the
molecular mechanisms governing α-phase formation near the
exten ded defects in 2H-MoS
2
and its inuence on the
subsequent transition to the 1T phase. Furthermore, our
large-scale MD simulations demonstrate the impact of
temperature on the size, shape, and concentration of 1T
phase domains in the monolayer. In addition, we observe that
such a transformation is absent in randomly distributed S-
vacancies in a MoS
2
layer. Overall, our study elucidates atomic-
scale dynamics associated with defect migration, provides a
mechanism for 2H-to-1T transformation, and outlines useful
design rules for engineering the properties of 2D materials by
deviating from their stoichiometric composition.
RESULTS AND DISCUSSION
Evolutionary Structural Optimization of Defects in
2D MoS
2
. We rst track the extended congurations of sulfur
vacancies in a monolayer MoS
2
by performing GA-based
structural optimization. Our search for extended congurations
made up entirely of S vacancies is well-founded in light of
recent experiments, which indicate that S vacancies are the
most dominant type of defects in MoS
2
sheets obtained via
mechanical exfoliation and chemical vapor deposition.
31
Furthermore, previous DFT calculations report that the
formation energies of S-vacancy (2.12 eV) are lower than all
other types of defects including anti-sites.
5
As mentioned here,
we start our GA runs with initial populations of candidates
containing randomly distributed S-vacancies at the desired
vacancy density. Figure 1 shows the evolution of defect
structures from randomly dispersed vacancies to ordered
extended congurations in a MoS
2
monolayer at four dierent
S-vacancy concentrations (ρ = 1.5, 4, 5 and 7.5%). The
potential energy of the most stable structure obtained at each
generation is plotted in Figure 1a, which converges in 600
generations for all of the cases. Parts beofFigure 1 depict the
atomic snapshots of initial randomly distributed S-vacancies
and nal optimized congurationsatvariousvacancy
concentrations. During the early stages of evolution (within
rst 100 generations), we observe formation of sm all
aggregates of vacancies, such as dimers and trimers. The
energetic gain in forming these aggregates is 0.001 eV/atom
for ρ = 1.5% and 0.018 eV/atom for the highest concentration
studied, i.e., ρ = 7.5%. The number of dimers and trimers is a
Figure 2. High-resolution TEM images showing the distribution of line defects in MoS
2
samples with dierent defect densities: (a) light, (b)
medium and (c) heavy. Extended line defects identied by our GA search are seen in this HRTEM images of MoS
2
. Defect distribution under
electron beam (50000 e
2
·s) are shown in (d) and (e) at time t = 0 s and t = 120 s, respectively. (f) Atomic-resolved HAADF-STEM
image of monolayer MoS
2
shows various defect congurations.
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strong function of the defect density and shows a non-
monotonic trend; the highest fraction of vacancies occurs in
the form of dimers/trimers (3%) for ρ = 7.5% after 130
generations. As the GA run proceeds further, we observe that
most of the vacancies exist as small line defects (34S
vacancies). Depending on the defect densities, we also observe
a rich variety of congurations, including triangular shapes
(Figure 1d) or zig-zag (Figure 1e). This is consistent with
previous experiments, which report the existence of triangular
holes,
32,33
ower shapes,
34
and amorphous networks,
35
along
with lines in electron-beam irradiated 2D materials. Addition-
ally, triangular holes formed by three missing neighboring
sulfur atoms (Figure 1d) suggest the possibility of a V
MoS3
phase in a MoS
2
layer as seen in our HRTEM; both of these
ndings are consistent with previous experimental works.
5
The
lowest energy structures obtained at the end of the GA runs
reveal extended line defects of sulfur vacancies (>10) to be the
most favorable at all vacancy concentrations considered in this
work (Figure 1be). The energies of the optimized defect
structures are 5.0034, 5.01844, 5.0195, and 5.00866 eV/atom
lower than the initial random population for ρ = 1.5%, 4.0%,
5.0%, and 7.5%, respectively.
The energy of the most stable structure is expected to
increase monotonically with defect concentration. Indeed, the
lowest energy of GA-optimized congurations, for ρ 4%,
follow this intuitive trend. At the lowest defect concentration
studied here (i.e., ρ = 1.5%,), however, the converged energy
value is higher than all of th e oth er cases, which is
counterintuitive. The GA-identied lowest energy congu-
ration (after 600 generations) for ρ = 1.5% consists of a
combination of lines (of varying sizes) and isolated vacancies
(cf. Figure 1b), which results in a somewhat higher energy
∼−5.0034 eV/atom. Ordering all of the vacancies in a single
line, for ρ = 1.5%, results in a drop of 17 meV/atom, yielding
an energy value of 5.021 eV/atom, lower than that of higher
defect concentrations (ρ 4%). Thus, the GA run for ρ =
1.5% does not reach the global energy minimum within 600
generations. Nevertheless, it is important to note that the
energetic dierence between the conguration shown in Figure
1b and the global minimum (17 meV/atom) is within the
thermal uctuations at room temperature. Thus, extended
defect congurations containing lines of dierent lengths (such
as that identied by GA in Figure 1b) are all likely to occur at
room temperature, alongside the global minimum structure.
This nding is rmly supported by our HRTEM images
(Figure 2), which show a range of defect congurations with
lines of varying lengths, along with isolated defects. We further
note that the slow convergence of GA for low defect
concentration case (i.e., extremal cases) is typical of most
ML methods.
36
High-ResolutionElectronMicroscopyonDefect
Evolution and Distribution in MoS
2
Samples. We
Figure 3. Role played by line defects in 2H-to-1T phase transition in MoS
2
. (a) Energy barrier associated with the 2H-1T transition.
29
(Inset)
Top and side view of the two phases are shown schematically. (b) Initial conguration of a line defect in a 2H-MoS
2
layer of dimension 5.8
nm × 5.2 nm. The line defect is shaded for clarity. (c) Evolution of Mo atoms proximal to line defect at 900 K. (d) S atoms in one plane glide
with respect to other leading to rapid shrinking of MoMo bonds near the line defect forming an intermediate α-phase. (e) Side view of S
atoms gliding over longer time scales results in 1T phase. Mo atoms are shown in red whereas atoms in yellow represent top layer of S and
atoms in blue represent the bottom layer of S.
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performed detailed characterization of the defect distribution
in 2D MoS
2
to validate the structural predictions made by our
GA. Three electro ablated monolayer MoS
2
region s with
dierent defect densities were imaged by HRTEM with a
large overfocus imposed to ensure the bright atom contrast and
easily distinguish the defects from perfect hexagonal lattice.
The structural defects evolve from randomly distributed sulfur
monovacancies (light defect density shown in Figure 2a) and
distributed line defects (medium density shown in Figure 2b)
to extended coupled line defect induced structural disorders
(heavily defective structure shown in Figure 2c). Suc h
HRTEM observations testify the GA prediction at dierent
defect densities in 2D MoS
2
and indicate a large variation in
the size of extended defects. We note that these defects are
intrinsic in the sample as the doses used for beam shower and
imaging are mild (5000 e
2
·s) and unlikely to create
knock-on damages. However, prolonged electron irradiation in
the monochromated TEM mode (50000 e
2
·s for 120s,
which is 1-fold higher than the imaging dose, demonstrated in
Figure 2ac) generates sulfur monovacancies due to the
knock-on damage.
37
This prolonged electron irradiation helps
randomly distributed sulfur monovacancies to evolve into
extended s tructural imperfections such as line defects,
triangular holes, and amorphous networks as shown in Figure
2d,e. Further, an atomic-resolution high-angle annular dark
eld scanning TEM (HAADF-STEM) image of the irradiated
monolayer MoS
2
in Figure 2fshowsvariousdefect
congurations such as sulfur monovacancies V
S
and triangular
defects V
MoS3
. Figure 2f also suggests the formation of an α-
phase due to extensive line defects, and coupling of two α-
phase regions at 60° to each other may trigger the formation of
1T domains in the 2H phase of MoS
2
.
16
Atomistic Simulations of Defect-Dri ven 2H-to-1T
Phase Transformation. Our HRTEM characterization
reveals a rich distribution of extended defects and hints at a
possible correlation between the defect densities and the
observed phases (2H, 1T and α). This correlation is also
observed for many other 2D materials.
31
Here, we aim to
understand this correlation for MoS
2
monolayers. The 2H
phase of MoS
2
exhibits ABA staking of atoms, while the atoms
are in an ABC staking in the 1T phase as shown in Figure 3a.
20
Both DFT a nd ReaxFF calculations suggest an energy
dierence of 0.5 eV per formula unit that exists between the
two phases, with 1T and 2H being the metastable and ground
states, respectively. Further, Nudged Elastic Band calculations
shown in Figure 3a indicate that an energy barrier of 1.25 eV
per formula unit needs to be surmounted in order to transform
from a 2H phase to a 1T phase.
20
On the other hand, the
Figure 4. Phase transformation on a MoS
2
layer with randomly distributed line defects. (a) Atomic snapshot after 1 ns of MD simulation at
900 K. The top view of the sheet is shown where blue regions represent extended defects, and yellow beads are the S atoms in the top layer.
Two zoomed regions in (a) are highlighted in (b) and (c) with atomic details. The coexistence of 2H, 1T, and α phases are demonstrated in
(b) where solid lines are guide to the eye. Further, 1T phases are shaded for clarity in (b) and (c). (d) Probability distribution of bonds
between Mo atoms and top layer S atoms at 900 K, where the bond lengths corresponding to 1T, 2H, and α are shown by arrow marks. (e)
Fraction of 1T, 2H, and α phases as a function of temperature.
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energy barrier for the 1T 2H phase transformation is 0.75 eV
per formula unit. Such barriers can be surmounted via heat
treatment, which in turn can yield coexistence of 2H and 1T
phases in the same sample.
19,38,39
This is especially important
considering the widely dierent electronic properties of the 2H
and 1T phases. Previous studies suggest that the trans-
formation between the 2H and 1T phase requires gliding of S
atoms in one plane with respect to the other; such gliding can
be achieved by thermal activation, and exposure to an electric
beam.
40
Here, we explore the eects of extended line defects
seen in our GA and HRTEM on the phase transformation
between the 2H and 1T phases. In particular, we perform MD
simulations to better understand how the gliding of atoms
takes place during the transformation and gain insights into the
atomic scale pathways via which the energy barrier is
surmounted in a MoS
2
layer during heat treatment. We rst
perform a series of controlled MD simulations on pristine
phases. Our MD simulations on the pristine 1T phase and 2H
phase do not show any transformation, regardless of the
temperature (cf. Figure S1, Supporting Information). Fur-
thermore, randomly distributed atomic defects on these two
phases do not induce a phase transformation (cf. Figure S2,
Supporting Information). Next, we perform MD simulations
on congurations with extended line defects. These simu-
lations demonstrate that phase transformation initiates only
when extended defects appear on a MoS
2
layer, which is
identied as the lowest energy conguration by our GA study.
We performed a series of MD simulations at dierent
temperatures starting with congurations that have randomly
distributed line defect(s) (similar to GA predictions) in a
MoS
2
layer. Parts beofFigure 3 illustrate the atomic-scale
mechanisms for the onset of the 2H-to-1T transition in a MoS
2
sheet with a single line defect, as identied by our MD
simulations. The initial conguration is entirely 2H containing
a line defect (Figure 3b), with a conguration similar to that
obtained from our evolutionary structural searches (Figure
1be). The temporal evolution of the region proximal to the
line defect is shown in Figure 3 c. We observe two types of
phase transformations that have widely dierent time scales.
There is an initial rapid formation of the so-called α phase near
the line defect within the rst 10 ps of the MD run. During this
α-phase formation, top S atoms from both sides of the line
defect glide toward the defect, as shown by the solid black
arrows in Figure. 3. The gliding of S atoms is concurrent with
the shrinking of Mo atomic lines in the middle layer of the
sheet (Figure 3d). Over much longer time scales (1 ns), the
1T phase starts to nucleate near the α region, which is
highlighted by shaded regions in the bottom panel of Figure
3c. In addition, the gliding of S atoms during the 1T phase
formation (side view) is shown by solid arrows in Figure 3e.
Such coexistence of the 2H, 1T, and α-phase is also seen in our
HRTEM experiment (cf. Figure 2).
In order to understand the kinetics associated with local
growth of the 1T phase and its stability, we perform large-scale
MD simulations where line defects are randomly placed in a
21.8 nm × 24.9 nm MoS
2
sheet. This large sheet of MoS
2
represents a distribution of extended line defects (identied by
GA) that are in close agreement with HRTEM images shown
in Figure 2. The equilibrium conguration of the large area
MoS
2
sheet is shown in Figure 4a for a representative
temperature (900 K). The system reaches a steady state within
1 ns, wherein 1T, 2H, and α phases coexist (Figure 4a,b).
Similar to the single-line defect system, we also observe
transformation of the 2H phase to 1T phase locally near the
line defects. In particular, discrete linear regions (one-
dimensional) of the 1T phase form next to the α-phase; a
representative region close to a line defect that transforms to
2H-α-1T is shown in Figure 4b. Furthermore, two-dimensional
growth of 1T phase is seen at the intersection of two-line
defects, as shown in Figure 4c. This observation is consistent
with the ndings of our HRTEM images (Figure 2f). Next, we
analyze the distribution and amounts of various phases as a
function of temperature. We use a distance criterion to
distinguish dierent phases after the MoS
2
layer reaches a
steady state at any given temperature. The Mo and S atoms
belonging to 1T, 2H, and α-phases are distinguished using the
shortest MoS separation distances (1T: 2.18 Å, 2H: 2.33 Å
and α: 2.45 Å). The detailed in-equilibrium congurations and
interatomic distances for various phases in a MoS
2
monolayer
can be found elsewhere.
20,41,42
The probability distribution of
dierent phases at 900 K is shown in Figure 4d. At 900 K, 14%
of MoS bonds correspond to the 2H phase, while 1.7% of the
MoS bonds correspond to the 1T phase. A large portion of
MoS bonds (26%) remains in the α-phase, which may
transform into the 1T phase over extended time scales not
accessible to MD simulations. Our simulations further suggest
that the relative proportions of the three phases can be
controlled by varying the temperature. For example, the
proportion of the 1T and 2H phase increases with temperature
as shown in Figure 4e. The data suggest that the rate of
increment in 1T phase is greater than that of 2H phase. The
increment in the proportion of the 2H and 1T phase is due to
the reduction of α-phase as temperature increases.
Figure 4e shows that the fraction of 1T phase is low (0.5%
2.5%) regardless of the temperature; nevertheless, even this
small amount of metal region has a signicant impact in device
application. It has the potential to signicantly decrease the
Schottky barrier and strong Fermi level pinning on the
extended defects.
9
Therefore, creating such a small domain of a
local conducting region is very important for many device
applications such as making a conducting lament in a large
TMD layer for neuromorphic devices. Furthermore, we expect
that the fraction of 1T phase can be tailored by changing the
distribution of extended defects, and alignment of extended
defects within a particular distribution. Our ndings clearly
demonstrate the possibility of controlling the size and shape of
1T phases by manipulating the defect densities, temperature,
and/or alignment of extended defects.
CONCLUSIONS
Evolution of point defects into extended defects and their role
in inducing phase transformation in an atomically thin sheet of
a TMD layer involves atomic processes that occur over a broad
range of time scales spanning picoseconds to several seconds.
Traditional experimental and simulation methods often fail to
provide a holistic understanding of such multiscale phenom-
ena. Here, we combine machine learning, molecular dynamics
simulations, and high-resolution electron microscopy to fully
understand phase transformation in a TMD layer. In particular,
we investigated the defect distribution and their role in driving
the 2H-to-1T phase transformation using MoS
2
as a model
TMD material. The genetic algorithm identies the aggrega-
tion of point defects (0D) into a line defect (1D) on a MoS
2
layer, which is the energetically most stable structure; such
aggregation of point defects into ordered line defects occurs
regardless of the vacancy concentration. These predictions are
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validated by our in situ HRTEM experiments. The HRTEM
experiments suggest a possible semiconductor (2H) to metal
(1T) phase transformation locally in the vicinity of the line
defect. We conduct MD simulations that elucidate the
molecular mechanism of this d efect-driven phase trans-
formation. Our simulations reveal that the S atoms glide
locally toward the defect sites and lead to the formation of an
intermediate α-phase. Th is α-phase triggers 1T phase
formation locally. We demonstrate that a typical 2H 1T
phase transformation in a MoS
2
layer is associated with
phenomena occurring over several dierent time scales: (i) a
long time, typically seconds and minutes, over which atomic
defects migrate and coalescence into extended line defects, (ii)
a rapid transformation of 2H to α-phase (10 ps) around
these extended line defects, and (iii) an intermediate time scale
(1 ns), over which the α-phase initiates the 2H 1T phase
transformation. The coalescence of point defects and
formation of 1T require activation energy, which is typically
provided through heating and electron beam radiation in
experiments. Therefore, by introducing line defects, the relative
proportions and the coexistence of metallic 1T and semi-
conducting 2H phases can be systematically tuned in an
atomically thin MoS
2
layer. Our HRTEM and MD simulations
suggest that the size and shape of the 1T regions is inuenced
by the alignment of the extended line defects. Overall, the
present study elucidates the defect aggregation and defect
driven phase transition mechanism in 2D TMD materials. This
has potential implications in fabricating electrical circuits in the
semiconducting MoS
2
monolayer for nanoscale electronic
applications. In addition, our work provides a generic
framework where machine learning can be combined with
molecular simulations and electron microscopy to study
multiscale processes associated with complex materials
phenomena.
METHODS
Over the past few years, machine learning and articial intelligence
based methods have advanced various facets of materials science,
including accelerated synthesis via robotics,
43
enhancing existing
material characterization methods,
44
searching for thermodynamically
stable structures,
45,46
materials design,
36,47
and developing accurate
atomistic models.
4850
In the context of 2D materials, such ML-based
techniques have enabled rapid searches for exfoliated 2D monolayers
and their assembly into superlattices/heterostructures
43
as well as
enhancing optical characterization of large-area 2D materials.
44
Simulation methods such as ab initio molecular dynamics (AIMD)
simulations, classical MD, and kinetic Monte Carlo simulations can be
used to understand defect dynamics. AIMD simulations due to their
high cost are limited in the time and length scales they can access.
Some of our recent studies push the limit of what can be achieved
with AIMD
5153
(we note that these simulations were performed on
Argonnes leadership computing and a single simulation required
10000 cores over 6 months for simulation time scales of few tens of
picoseconds). Clearly, studies of defect dynamics (approximately
several nanoseconds and longer) remain intractable with AIMD.
Kinetic Monte Carlo is a powerful mesoscale technique to access
much larger length scales and longer time scales but relies on
knowledge of a predened rate catalog; i.e., mechanisms have to be
known a priori.
54,55
Classical MD overcomes these limitations and
allows us to understand extended defect dynamics over nanometer/
nanosecond scales. While there are reports of machine learning
enhanced molecular dynamics (MD) simulations (i.e., the use of
machine learning to develop accurate interatomic potentials for use in
MD simulations), this work uses machine learning to perform
structural optimization and evolution of the point defects into
extended structures. Essentially, this work involves use of GA to
sample congurations of defect structures to identify ones that are
energetically favorable; in the case of our target system MoS
2
, the line
defects (ordered vacancies) are more stable than isolated vacancies
(i.e., point defects). For instance, GA has been used to obtain optimal
potential parameter sets for a bond-order potential to describe
interactions in CoC heterostructures.
50
Similarly, Csa
́
nyi et al.
56
employ machine le arning to c onstruct force-eld models for
amorphous silicon, while Ramprasad et al.
48
provide a perspective
on the use of machine learning to develop interatomic potentials for
various materials. In short, these works (and other related report)
involve designing strategies for ecient parameter optimization, while
we are focused on deriving the most stable structural conguration of
extended defects.
It should be noted that structural optimization via GA has also
been used for 2 D science mainly for crystal-structure predic-
tion.
36,47,5759
In most studies, genetic algorithm (GA) in
combination with density functional theory (DFT) is used to search
the global minimum structures. A typical GA run would involve 20
populations run over 100 generations (total 2000 evaluations per
system). Owing to the computational cost of DFT, these studies
involve system sizes of single to few unit cells. In order to use GA to
predict extended defect structures such as the line defects (that
extended to several nanometers), one requires a system size that is
much larger (supercell 20 × 18360 unit cells). This is
computationally intractable with DFT. Empirical force-elds with
much lower cost allow us to eciently sample the defect
congurations. Hence, we use GA and MD to understand defect
dynamics of extended structures.
Similarly, th ere have been previous eorts on advancing
microscopy techniques to characterize defect dynamics. For example,
in a seminal work, Hashimoto et al.
60
show in situ defect formation in
single graphene layers by high-resolution TEM. Meyer et al.
61
represent a major advance in using TEM to image the dynamics of
light atoms and molecules on graphene. Likewise, Sim et al.
27
employs
electron microscopy studies to investigate how defect structures in
multilayered 2D materials dier from their monolayers. While such
electron microscopy studies can capture temporal evolution, their
resolution is still limited to frame speeds 10 Hz and consequently
cannot capture short-lived events (nanosecond time scales). Such
ultrafa st dynamica l events are cru cial for de fec t- drive n phase
transitions between semiconducting and metallic phases in TMDCs
(e.g., MoS
2
). Overall, it is not possible for a single technique to probe
the dynamics occurring over disparate time and length scales.
Here, ML methods are combined with molecular dynamics
simulations and model validation is performed via HRTEM
experiments to obtain a holistic picture of how point defects organize
into extended structures, which subsequently drive the 2H-to-1T
transition. This understanding cannot be provided by a single method
alone since the time scales involved in defect dynamics vary from
picoseconds (too fast for HRTEM) to several minutes (too long for
MD). By using HRTEM, GA, and MD simulations, we show the
defect evolution from randomly distributed point defects to extended
line defects and highlight their role in driving the 2H to 1T phase
transitions in 2D MoS
2.
Specically, we employ GA to identify
extended defect structures that form via organization of point defects;
the GA-identied structures are validated by HRTEM. Molecular
dynamics simulations, alongside HRTEM, elucidate (a) that extended
defect structures act as precursors for 2H-to-1T transition and (b) the
coexistence of 2H and 1T phases in a single monolayer. In all machine
learning studies, model validation is an important aspect and HRTEM
serves this important purpose of validating the predictions of GA. In
the subsequent sections, we provide the details of the three
techniques.
Evolutionary Structural Search. Evolutionary searches identify
the global energy minimum structure of a material along with
structures that are energetically close (but higher) than the most
stable structure; often, such structures are kinetically trapped
depending on processing and operating condition of the material.
Therefore, this method is widely used in materials design
problems.
36,62,63
Here, we adopt an evolutionary search, viz., genetic
ACS Nano Article
DOI: 10.1021/acsnano.8b02844
ACS Nano 2018, 12, 80068016
8012
algorithms (GA) to identify energetically favorable arrangements of
vacancies in one of the S planes of a MoS
2
layer. In GA, candidate
materials structures are mapped to a genome upon which the
evolutionary operations are employed. In a single layer MoS
2
, a plane
of Mo atoms is sandwiched between two planes of S atoms; in each S
plane, the atoms are organized in a 2D triangular lattice. As the
interlayer vacancy migration is associated with a very high energy
barrier (>5 eV), we restrict our search space to the top layer of S
atoms. To describe the vacancy distribution in a given candidate
structure, we dene a 2D binary genome. This genome is a string
containing the current state for each site in the 2D triangular lattice;
each site can be in one of the two states, namely: (a) 0 representing
the absence of a S atom (vacancy) and (b) 1 indicating that site is
occupied by a S atom. For a prescribed vacancy density, the
evolutionary search begins with a random population of 32
candidates, each with an arbitrarily chosen but distinct genome,
(i.e., S-vacancy distributions). The tness of each candidate is
calculated as the potential energy of the MoS
2
monolayer containing a
distribution of S-vacancies as dened by its 2D genome. We note that
the candidate structures with lower potential energy possess higher
tness, and have higher chance of survival in an evolution. The atomic
interactions in the defective MoS
2
structures are modeled using the
reactive force eld (ReaxFF)
20
within LAMMPS
64
package. In each
generation, genetic operations, namely, selection, mutation, and
crossover, are performed on the current population to generate 32
new candidates; details of these operations are provided else-
where.
36,47
The candidates are then ranked by their tness, and the
best (ttest) 32 candidates are passed to the next generation. This
procedure is iterated until the GA run converges; i.e., the potential
energy of the ttest candidate does not change over a long period of
time (100 generations). We note that several case studies are
conducted with varying number of population size, and 32 is found to
be suciently large to ensure necessary structural diversity in the
population (in the initial stages) as well as convergence to low-energy
congurations with reasonable computational costs. Our evolutionary
searches using population sizes (>32) have resulted in identical lowest
energy congurations, as that from runs with 32 candidates in the
gene pool. Moreover, the 2D MoS
2
sheet used for sampling defect
congurations is suciently large (5.2 nm × 5.8 nm) to avoid nite
size eects; using a MoS
2
sheet with twice the area yielded identical
congurations after convergence of GA runs.
Molecular Dynamics Simulations. To investigate the atomic-
scale mechanisms underlying early stages of 2H-to-1T phase
transition in monolayer MoS
2
, we employed isobaricisothermal
(NPT) MD at various temperatures (3001500 K) and ambient
pressure. All MD simulations are performed using the LAMMPS
64
package. Defective monolayer MoS
2
sheets (up to 21.8 nm × 24.9
nm; 17140 atoms) are prepared by pla cing the GA- derived
energetically favora ble extended vacancy congurations (most ly
lines) along random orientations in one S-plane. Periodic boundary
conditions are employed in the plane of the MoS
2
sheet. Similar to the
GA searches, the atomic interactions are described by ReaxFF.
20
Constant temperature and pressure conditions are maintained using a
Nose
́
Hoover thermostat and barostat.
65
Sample Preparation and High-Resolution Transmission
Electron Microscopy. Single-layer MoS
2
samples were prepared
through an electrochemical thinning process, known as electro-
ablation (EA), using the procedure reported by Das et al.
66
In the EA
process, multilayer/bulk MoS
2
akes are mechanically exfoliated onto
a conductive TiN substrate where a 1.4 V vs Ag/AgCl potential was
applied for <60 s. During the substrate-assisted, self-limited EA, the
multilayer akes undergo an electro-oxidation process which ablates
away the bulk layers leaving the bottom monolayer intact. TMDs
produced via EA have shown excellent semiconducting properties in
eld eect transistor (FET) devices; however, photoluminescence
studies have shown that excessive EA times introduce signicant
numbers of defects such as sulfur vacancies. Since the ablation
initiates at the edge sites and therefore material ablates rst from the
perimeter working inward toward the center of the ake, the outer
edges are exposed to the EA process for longer periods of time.
6769
Hence, an inhomogenous defect density is observed as seen in Figure
2 with the edge regions being more defective than the center. The
electroablated exfoliated MoS
2
akes were transferred by an etchant
free transfer method
70
from the TiN substrate onto a Au Quantifoil
TEM grid for TEM analyses; in this technique, most residues are
washed away by several water baths to avoid contamination.
Aberration corrected scanning/TEM (AC-S/TEM) imaging was
performed on a FEI Titan
3
60300 microscope at 80 kV accelerating
voltage with a monochromated gun and spherical aberration corrected
lenses, providing subangstrom resolution. The electron dose of 5000
e
2
·s was used for HRTEM imaging of monolayer MoS
2
to
minimize structural damage and to push away possible contaminants.
The high-angle annular dark eld (HAADF) detector (Fischione)
which was used for ADF-STEM imaging acquisition had a beam
current of 45pA, beam convergence angle of 30 mrad, and collection
angle of 51300 mrad. The HRTEM and ADF-STEM images in the
content are further ltered by Gaussian blur function via ImageJ
software.
ASSOCIATED CONTENT
*
S
Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acsnano.8b02844.
Details of the MD simulations performed for 2D MoS
2
(pristine as well as with sulfur defects) (PDF)
AUTHOR INFORMATION
Corresponding Authors
*E-mail: sud70@psu.edu.
*E-mail: badri.narayanan@louisville.edu.
*E-mail: skrssank@anl.gov.
ORCID
Daniel S. Schulman: 0000-0002-0751-0578
Henry Chan: 0000-0002-8198-7737
Mathew J. Cherukara: 0000-0002-1475-6998
Saptarshi Das: 0000-0002-0188-945X
Badri Narayanan: 0000-0001-8147-1047
Subramanian K. R. S. Sankaranarayanan: 0000-0002-9708-
396X
Present Address
B.N.: Department of Mechanical Engineering, University of
Louisville, Louisville KY 40292
Author Contributions
S.D., B.N., and S.K.R.S. conceived this project. T.P. carried out
the GA optimization and MD simulations. F.Z. and D.S.
carried out the experiments. All the authors contributed to the
data analysis. S.K.R.S., B.N., and T.P. wrote this manuscript
with contribution from all the authors. All authors have given
approval to the nal version of the manuscript.
Notes
The authors declare no competing nancial interest.
ACKNOWLEDGMENTS
This work was supported by Argonne LDRD-2017-012-N0.
Use of the Center for Nanoscale Materials and the resources of
the Argonne Leadership Computing Facility was also
supported by the U.S. Department of Energy (DOE), Oce
of Science, Oce of Basic Science, under Contract No. DE-
AC02-06CH11357. This research used resources of the
National Energy Research Scientic Computing Center, a
DOE oce of science user facility supported by the Oce of
Science of the US Department of Energy under Contract No.
DE-AC02-05CH112 31. An award of computer time was
ACS Nano Article
DOI: 10.1021/acsnano.8b02844
ACS Nano 2018, 12, 80068016
8013
provided by the Innovative and Novel Computational Impact
on Theory and Experiment (INCITE) program. This research
used resources of the Argonne Leadership Computational
Facility, which is a DOE Oce of Science user facility
supported under Contract No. DE-AC02-06CH11357. T.K.P.
thanks Prof. David Simmons, University of Akron, for
providing the GA code, which is modied and used for this
work. D.S.S. and S.D. acknowledge support from the Air Force
Oce of Scientic Research (AFOSR) through the Young
Investigator Program with Grant No. FA9550-17-1-0018. F. Z.
and M. T. acknowledge th e NSF-IUCRC Center for
Atomically Thin Multifunctional Coatings 275 (ATOMIC),
under award #1540018.
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